Bacteria commonly swim through complex biological fluids like mucus, playing a crucial role in health and disease, from infections in the lungs to microbial imbalances in the gut. Understanding how bacteria move through biological fluids is the first step toward developing new ways to cure and prevent such infections. Many mathematical tools describing how microorganisms swim through fluids like water were developed in the 1950s-1970s. These foundational theories continue to be used today. However, mucus is a far more complex and challenging environment than water. It is composed of macromolecular proteins (mucins) that confer it viscoelastic properties, simultaneously flowing like a fluid, yet capable of recoiling like elastic solids. Mathematical tools for studying bacterial locomotion through such complex biological fluids are lacking. This research will combine mathematics, computer simulations, and laboratory experiments to create a more comprehensive picture of this process. It will first investigate the fluid mechanics of propulsion through complex fluids using a single bacterial flagellum. This will be followed by a study of how multiple flagella bundle together, a standard feature of many bacteria like E. coli. Finally, the collective behavior of large groups of bacteria in fluids like mucus will be investigated. Knowledge so gained will be instructive in the design of new medicines, the prevention of dangerous infections of mucosal surfaces, and in the management of